Mathematical Sciences: Problems in Function Theory and Operator Theory

数学科学：函数论和算子理论问题

• 批准号: 9005988
• 负责人: Barbara MacCluer
• 金额: $ 3.07万
• 依托单位: University of Richmond
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9005988&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Function; Theory

This research concerns several problems which lie at the interface of operator theory and function theory. The first part of the project involves polynomial approximation directed at understanding certain measures on the closed unit disc. The other part of the project involves a study of the composition operators on various spaces of analytic functions. This includes work on identifying the spectrum of a composition operator, continuing work on the study of composition operators on large weighted Bergman spaces, and the question of identifying the components in the space of composition operators in the uniform operator topology. This research is in the general area of modern analysis and, as noted above, lies at the interface of operator theory and function theory. The research involves the study of composition operators on spaces of analytic functions in one or several complex variables and is a central topic in the modern theory of complex analysis.

本研究涉及的几个问题， 算子论与函数论的接口。 第一部分 该项目涉及多项式逼近， 了解封闭式机组圆盘上的某些措施。 的 该项目的另一部分涉及研究的组成 各种解析函数空间上的算子。 这包括 致力于识别复合算子的谱， 继续研究大规模的复合算子 加权Bergman空间，以及确定 复合算子空间中的分量 算子拓扑 这项研究属于现代分析的一般领域， 如上所述，位于算子理论的界面， 功能理论 这项研究涉及到对作文的研究 一个或多个解析函数空间上的算子 复变量，是一个中心议题，在现代理论， 复分析